The missing measure m is approximately 8.83 and the missing angle, angle N, is 62.1 degrees.
To solve this problem, we can use the trigonometric functions sine (sin), cosine (cos), and tangent (tan). These functions relate the sides and angles of a right triangle.
Step 1: Identify the sides of the triangle
The side opposite the angle of 28 degrees is labeled N. The side adjacent to the angle of 28 degrees is labeled m. The hypotenuse is the longest side of the triangle, and it is opposite the right angle. In this case, the hypotenuse is labeled MAN.
Step 2: Choose the appropriate trigonometric function
We want to find the side m, which is adjacent to the angle of 28 degrees. Therefore, we can use the cosine function (cos).
Step 3: Write down the trigonometric equation
The cosine function is defined as the adjacent side over the hypotenuse. In this case, we have:
cos(28°) = m / MAN
Step 4: Solve for the missing measure
We know that cos(28°) is approximately 0.883. We can also substitute the known value of MAN into the equation.
0.883 = m / 10
Multiplying both sides of the equation by 10, we get:
m = 10 * 0.883
m = 8.83
Therefore, the missing measure m is approximately 8.83.
The image you sent shows a right triangle with a missing angle. The triangle has the following labels:
Angle L: 28 degrees
Angle N: Missing angle
Side M: Opposite angle N
Side MAN: Hypotenuse
We are asked to find the missing angle, angle N.
To solve this problem, we can use the following trigonometric identity:
sin(L) = cos(N)
This identity states that the sine of one angle in a right triangle is equal to the cosine of the complementary angle.
In this case, we know the sine of angle L, which is 28 degrees. We can use this information to find the cosine of angle N, which is the missing angle.
cos(N) = sin(L) = sin(28 degrees) = 0.469
Now that we know the cosine of angle N, we can use the inverse cosine function (also known as the arccosine function) to find angle N itself.
N = arccos(0.469) = 62.1 degrees
Therefore, the missing angle, angle N, is 62.1 degrees.